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Shape Analysis and Retrieval. Extended Gaussian Images. Notes courtesy of Funk et al. , SIGGRAPH 2004. Extended Gaussian Image. Represent a model by a spherical function by binning surface normals. Model. Angular Bins. EGI. Subdividing the Sphere. 20 Faces Icosahedron. 80 Faces.

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Shape analysis and retrieval

Shape Analysis and Retrieval

Extended Gaussian Images

Notes courtesy of Funk et al., SIGGRAPH 2004


Extended gaussian image
Extended Gaussian Image

  • Represent a model by a spherical function by binning surface normals

Model

Angular Bins

EGI


Subdividing the sphere
Subdividing the Sphere

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces

All bins have the same area


Hierarchical search
Hierarchical Search

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces


Hierarchical search1
Hierarchical Search

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces


Hierarchical search2
Hierarchical Search

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces


Hierarchical search3
Hierarchical Search

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces


Hierarchical search4
Hierarchical Search

20 FacesIcosahedron

80 Faces

320 Faces

1280 Faces


Angular parameterization
Angular Parameterization

4x4 Bins

8x8 Bins

16x16 Bins

32x32 Bins

Different bins have different areas


Angular parameterization1
Angular Parameterization

Missing node where bins are small

  • Different bins have different areas

    • Smaller bins lose their votes


Angular parameterization2
Angular Parameterization

Normalize bins by bin area


Extended gaussian image1
Extended Gaussian Image

  • Properties:

    • Invertible for convex shapes

    • 2D array of information

    • Can be defined for most models

Point Clouds

Polygon Soups

Closed Meshes

Genus-0 Meshes

Shape Spectrum


Extended gaussian image2
Extended Gaussian Image

  • Properties:

    • Invertible for convex shapes

    • 2D array of information

    • Can be defined for most models

  • Limitations:

    • Too much information is lost

    • Normals are sensitive to noise

3D Model

EGI


Extended gaussian image3
Extended Gaussian Image

  • Properties:

    • Invertible for convex shapes

    • 2D array of information

    • Can be defined for most models

  • Limitations:

    • Too much information is lost

    • Normals are sensitive to noise

Initial Model

Noisy Model


Retrieval results
Retrieval Results

Princeton Shape Benchmark:(~900 models, ~90 classes)

14 biplanes

50 human bipeds

7 dogs

17 fish

16 swords

6 skulls

15 desk chairs

13 electric guitars

http://www.shape.cs.princeton.edu/benchmark/


Retrieval results1
Retrieval Results

Precision

Recall


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